The global positioning system is a space-based, worldwide, all-weather passive radio positioning and timing system which was developed and implemented over the past two decades. The system is originally designed to provide precise position, velocity, and timing information on a global common grid system to an unlimited number of adequately equipped air, land, sea, and space authorized users and civil users.
The global positioning system user equipment, which consists of an antenna, a signal processing unit, and associated electronics and displays, receives the signals from the global positioning system satellites to obtain position, velocity, and time solution. The global positioning system principle of operation is based on range triangulation. Because the satellite position is known accurately via ephemeris data, the user can track the satellite's transmitted signal and determine the signal propagation time. Since the signal travels at the speed of light, the user can calculate the geometrical range to the satellite. The actual range measurement (called the pseudorange) contains errors, for example bias in the user's clock relative to global positioning system reference time. Because atomic clocks are utilized in the satellites, their errors are much smaller in magnitude than the users' clocks. Thus, for three-dimensional position determination, and also to calculate the cock bias, the pure global positioning system needs a minimum of four satellites to obtain a navigation solution.
Global positioning system contains a number of error sources: the signal propagation errors, satellites errors, and the selective availability. The user range error (URE) is the resultant ranging error along the line-of-sight between the user and the global positioning system satellite. Global positioning system errors tend to be relatively constant (on average) over time, thus giving global positioning system long-term error stability. However, the signals of the global positioning system may be intentionally or unintentionally jammed or spoofed, or the global positioning system receiver antenna may be obscured during vehicle attitude maneuvering. The global positioning system signals are lost when the signal-to-noise ratio is low and the vehicle is undergoing highly dynamic maneuvers.
An inertial navigation system comprises an onboard inertial measurement unit, a processor, and an embedded navigation software. The positioning solution is obtained by numerically solving Newton's equations of motion using measurements of vehicle specific forces and rotation rates obtained from onboard inertial sensors. The onboard inertial sensors consist of accelerometers and gyros which together with the associated hardware and electronics comprise the inertial measurement unit.
The inertial navigation system may be mechanized in either a gimbaled or strapdown configuration. In a gimbaled inertial navigation system, the accelerometers and gyros are mounted on a gimbaled platform to isolate the sensors from the rotations of the vehicle, and to keep the measurements and navigation calculations in a stabilized navigation coordinated frame. Possible navigation frames include earth centered inertial (ECI), earth-centered-earth-fix (ECEF), locally level with axes in the directions of north, east, down (NED), and locally level with a wander azimuth. In a strapdown inertial navigation system, the inertial sensors are rigidly mounted to the vehicle body frame, and a coordinate frame transformation matrix (analyzing platform) is used to transform the body-expressed acceleration and rotation measurements to a navigation frame to perform the navigation computation in the stabilized navigation frame. Gimbaled inertial navigation systems can be more accurate and easier to calibrate than strapdown inertial navigation systems. Strapdown inertial navigation systems can be subjected to higher dynamic conditions (such as high turn rate maneuvers) which can stress inertial sensor performance. However, with the availability of newer gyros and accelerometers, strapdown inertial navigation systems are becoming the predominant mechanization due to their low cost and reliability.
Inertial navigation systems in principle permit pure autonomous operation and output continuous position, velocity, and attitude data of vehicle after initializing the starting position and initiating an alignment procedure. In addition to autonomous operation, other advantages of inertial navigation system include the full navigation solution and wide bandwidth. However, an inertial navigation system is expensive and subject to drift over an extended period of time. It means that the position error increases with time. This error propagation characteristic is primarily caused by its inertial sensor error sources, such as gyro drift, accelerometer bias, and scale factor errors.
The inherent drawbacks of a stand-alone inertial navigation system and a stand-alone global positioning system show that a stand-alone inertial navigation system or a stand-alone global positioning system can not meet mission requirements under some constraints such as low cost, high accuracy, continuous output, high degree of resistance to jamming and high dynamic.
In the case of integration of global positioning system with inertial navigation system, the short term accuracy of the inertial navigation system and the long term stability and accuracy of global positioning system directly complement each other.
One of integration approaches of global positioning system and inertial navigation system is to reset directly the inertial navigation system with global positioning system-derived position and velocity. The second approach is the cascaded integration where the global positioning system-derived position and velocity are used as the measurements in an integration Kalman filter. These two integration modes are called loosely-coupled integration. The third approach uses an extended kalman filter to process the raw pseudorange and delta range measurements of the global positioning system to provide optimal navigation parameter error estimates of the inertial navigation system, inertial sensor errors, and the global positioning system receiver clock offset. This approach is called tightly-coupled integration.
The shortcomings of the above-mentioned integration approaches are:
1. In the conventional global positioning system and inertial navigation system integration approaches, only position and velocity derived by global positioning system receiver or global positioning system raw pseudorange and delta range measurements are used. In fact, the raw carrier phase measurements of global positioning system have the highest measurement accuracy, but are not employed to contribute to an integration solution due to the difficulty of resolving the carrier phase ambiguity.
2. A significant impediment to the aiding of global positioning system signal tracking loops with inertial navigation system is that the aiding causes potential instability of the conventional global positioning system and inertial navigation integration system because there is a positive feedback signal loop in the combined global positioning and inertial system. The accuracy degradation of the inertial aiding data increases the signal tracking errors. The increased tracking errors fed to the inertial system may cause further degradation of inertial system because the measurements may severely affect the Kalman filter, which is well tuned for a low accuracy inertial navigation system.
3. In conventional tightly-coupled global positioning and inertial integration system, low accurate inertial sensor can not provide global positioning system satellite signal carrier phase tracking with velocity aiding because the aiding of carrier phase tracking loop requires high accuracy of external input velocity.
4. The conventional loosely-coupled global positioning and inertial integration system requires at least four global positioning system satellites available because a global positioning system processor requires at least four global positioning system satellites to derive the vehicle position and velocity, which are used in the loosely-coupled integration algorithm. This constraints the application of the loosely-coupled integration system. The second shortage of the loosely-coupled integration system is its bad dynamic performance because of without aiding of global positioning system code tracking from the external sensor.
5. The conventional global positioning and inertial integration processing has a poor vertical measurement accuracy.